"The point here is that for DoF purposes it is the format of the image that is actually used in the process of making a print that has a direct bearing on the final DoF perception. "

I think this is what Howie has been saying all along. This now becomes clear to me that the word format can mean different things in different contexts or conventions. If you ask most photographers "What format do you shoot?" they would answer 35 FF, 645 6x7 8x10 etc and the common understanding is that those are the dimensions of the image acquisition area. In the sentence I quote, you are using the word to refer to the actual image used - therein lies almost all this discussion which seems to revolve around a simple semantic issue here - if you define "format" that way, I suspect Howie would agree...[a href=\"index.php?act=findpost&pid=81054\"][{POST_SNAPBACK}][/a]

Andy,I think professional and large format photographers have always been used to having a choice of different backs with their cameras. The concept of reducing the format of your camera by reducing the size of the film in the back is only novel to some 35mm users who don't have that choice. I'm sure Howard understands there is no useful distinction to be made between sliding a 6x7cm film holder in the back of a 4x5 camera and using a 4x5" piece of film and cropping it later to 6x7cm. (Except economically, of course. Using a 4x5" piece of film when a 6x7cm piece will do, is very wasteful.)

What is generally referred to as the format of a camera could more precisely be defined as the maximum image size the camera allows you to capture, and that's something that Howard needs to know and does know I'm sure. When Howard picks up his 4x5 camera for a day's shooting, he knows he's got a 4x5 camera and a film holder containg 4x5 film (unless he's totally drunk), and he knows he can not measure the dimensions of any object in his viewfinder which are larger than 5".

Howie, from your response to my final challenge it is clear to me now that we are both using the same formulae, and as is the way with these things sometimes, have trouble agreeing on how to express them in English. We do not disagree on the mathematics, only on how to say it in words.

The only matter that remains to be resolved (or not) is whether it bothers you that the more common way of expressing these things will cause you to get annoyed at everyone else's stupidity.

At any rate I have been forced to examine the issue more closely, have learned a few things, and enjoyed the exchange.

I apologize for for being angry. That is not appropriate. There is a proverb I need to apply:

Proverbs 19, verse 20, "Get all the advice and instruction you can, and be wise the rest of your life."

Let's try this.

The hyperperfocal distance is well accepted to be:

h = f**2/(N*c)

where h is the hyperfoacal distance, f is the lens' focal length, n is the f/stop and c is the circle of confusion diameter on the film.

This equation can be rearrnaged to:

c = f**2/(N*h)

I hope we can all agree that all the terms on the right hand side of the equation are related to the lens and have nothing to do with camera format. In fact, the lens need not even be on a camera and the c could be measured off a wall, or sidewalk, or whereever the image is focused. Then, since c is determined be non-format dependant factors, it must also be format independant.

The photographer can change N to adjust c once set up and f and the focus distance is set. Then DoF can be determined by:

df = d*h/(h-d)

where df is the far limit of DoF, d is the focus distance, and h is the hyperfoacal distance. I have used a simplified version of the equations for d much much greater than f so d+/-f is essentially d.

The near limit of DoF dn is:

dn = d*h/(h+d)

DoF is the difference between df and dn.

Note: When h=d, dn is h/2 or half the focus distance. Hence, the notion that DoF is equally divided on either side of the hyperfocal distance.

I hope we can agree that so far camera format (or even a camera) hasn't entered. But CoC only matters on the print. Now the c on the format independant film must be put on paper. Usually enlarged. So:

CoC on the print = c * enlargement.

The degree of enlargement is also independant of film format. I think we can all agree that any sized print can be made from any sized negative. No need to be stuck with 30cm.

Same with viewing distance. The greater the viewing distance, the greater CoC will need (or can) be to be just seen as a point on the print. So CoC is variable for viewing ditance and we need not be stuck with 50cm.

The format size determines how much of the tree is on the negative, and that has nothing to do with DoF. If I trim an 8x10 neagtive to a 4x5, do I change anything on the negative? Of course not. [a href=\"index.php?act=findpost&pid=81072\"][{POST_SNAPBACK}][/a]

This is the sort of reasoning that I find bizarre. It's almost like saying, 'if I chop off an arm or a couple of feet, do I change your appearance'.

If you trim the negative before making a print, you have definitely changed the negative. You've removed some of it. If you make 2 prints of equal size, one from the trimmed negative and one from the full negative, you are quite likey going to have prints with different DoFs. Even if you make different size prints by enlarging the elements that are common to both images by the same degree, you can still have the perception of different DoFs, even though the DoF of the elements that are common to both prints is the same.

For example, if the full shot of the tree contains some buttresses (above ground roots) which are out-of-focus because I made a mistake with my DoF calculations or adjustments, I might decide to crop that part of the negative. (We all know that stuff in the foreground that's OoF is often not acceptable.) By cropping away the 'mistakes', I create a different composition, perhaps as good, perhaps not as good, but one which now has the correct or acceptable DoF.

On the other hand, the reason for cropping might not be to correct a mistake. If I have a fixed format camera, a prime lens with a fixed aperture and not much room to change my distance to the tree, I might well make the choice to sacrifice part of the negative, or use a smaller format (a film holder with a 6x7cm piece of film, if I have one).

To put it another way, from the perspective of the viewer of a print, DoF is correct, satisfacory, acceptable or not, as the case may be, only in relation to the format used. Changing format does not change the hypothetical range of distances where elements will be OoF by the specified degree in accordance with the rules of DoF but it does make the settings of f stop, distance to subject and choice of focal length either appropriate or not appropriate for the composition.

It's my view that the confusion in this thread results from a failure to distinguish clearly between the perception of DoF on the finished print and the hypothetical, imaginary DoF described by the mathematics, which of course must remain imaginary. I don't believe I have ever captured infinity on sensor or film, yet the DoF tables will often tell me that everything is sharp from x feet to infinity.

I apologize for for being angry. That is not appropriate. There is a proverb I need to apply:

Proverbs 19, verse 20, "Get all the advice and instruction you can, and be wise the rest of your life."

Let's try this.

The hyperperfocal distance is well accepted to be:

h = f**2/(N*c)

where h is the hyperfoacal distance, f is the lens' focal length, n is the f/stop and c is the circle of confusion diameter on the film.

This equation can be rearrnaged to:

c = f**2/(N*h)

I hope we can all agree that all the terms on the right hand side of the equation are related to the lens and have nothing to do with camera format. In fact, the lens need not even be on a camera and the c could be measured off a wall, or sidewalk, or whereever the image is focused. Then, since c is determined be non-format dependant factors, it must also be format independant.

The photographer can change N to adjust c once set up and f and the focus distance is set. Then DoF can be determined by:

df = d*h/(h-d)

where df is the far limit of DoF, d is the focus distance, and h is the hyperfoacal distance. I have used a simplified version of the equations for d much much greater than f so d+/-f is essentially d.

The near limit of DoF dn is:

dn = d*h/(h+d)

DoF is the difference between df and dn.

Note: When h=d, dn is h/2 or half the focus distance. Hence, the notion that DoF is equally divided on either side of the hyperfocal distance.

I hope we can agree that so far camera format (or even a camera) hasn't entered. But CoC only matters on the print. Now the c on the format independant film must be put on paper. Usually enlarged. So:

CoC on the print = c * enlargement.

The degree of enlargement is also independant of film format. I think we can all agree that any sized print can be made from any sized negative. No need to be stuck with 30cm.

Same with viewing distance. The greater the viewing distance, the greater CoC will need (or can) be to be just seen as a point on the print. So CoC is variable for viewing ditance and we need not be stuck with 50cm.

I apologize for for being angry. That is not appropriate. There is a proverb I need to apply:

Proverbs 19, verse 20, "Get all the advice and instruction you can, and be wise the rest of your life."

Let's try this.

The hyperperfocal distance is well accepted to be:

h = f**2/(N*c)

where h is the hyperfoacal distance, f is the lens' focal length, n is the f/stop and c is the circle of confusion diameter on the film.

This equation can be rearrnaged to:

c = f**2/(N*h)

I hope we can all agree that all the terms on the right hand side of the equation are related to the lens and have nothing to do with camera format. In fact, the lens need not even be on a camera and the c could be measured off a wall, or sidewalk, or whereever the image is focused. Then, since c is determined be non-format dependant factors, it must also be format independant.

The photographer can change N to adjust c once set up and f and the focus distance is set. Then DoF can be determined by:

df = d*h/(h-d)

where df is the far limit of DoF, d is the focus distance, and h is the hyperfoacal distance. I have used a simplified version of the equations for d much much greater than f so d+/-f is essentially d.

The near limit of DoF dn is:

dn = d*h/(h+d)

DoF is the difference between df and dn.

Note: When h=d, dn is h/2 or half the focus distance. Hence, the notion that DoF is equally divided on either side of the hyperfocal distance.

I hope we can agree that so far camera format (or even a camera) hasn't entered. But CoC only matters on the print. Now the c on the format independant film must be put on paper. Usually enlarged. So:

CoC on the print = c * enlargement.

The degree of enlargement is also independant of film format. I think we can all agree that any sized print can be made from any sized negative. No need to be stuck with 30cm.

Same with viewing distance. The greater the viewing distance, the greater CoC will need (or can) be to be just seen as a point on the print. So CoC is variable for viewing ditance and we need not be stuck with 50cm.

Forgot to add, if you know the degree of enlargement is going to be large (perhaps due to cropping), you might want to adjust your personally selected CoC accordingly. These factors, beins subjective, are not cast in concrete.

Image planning seldom takes into account I am making a mistake in plnning. If I knew that, I would just correct the plan. There may be times that the phyical reality of the subject's dimensions will not be the same as the plan you made (the tree grew). Then you may need to replan, not just change the degree of enlargment and crop.

I have been lurking this thread from the beginning, wondering how much anyone could possibly have to say about DOF in this day and age.

A friend of mine just getting into photography some 40 years ago felt quite guilty about having a hard time understanding explanations of DOF that she had heard. I think if she read this entire, massive thread today, she might feel better. And I think Proust would be proud of all of you.

For a while you all seemed a bit like the blind men describing an elephant, but eventually -- to me, anyway -- the views on both sides became clearer. At this point I'm tempted to say "you're both right."

Like the farmer listening to a political debate: After each politician spoke, the farmer turned to his neighbor and said, "By golly, he's right!" After the second such comment, the neighbor said, "But they can't both be right, can they?" To which the farmer replied, "By golly, you're right, too!"

My apologies to any farmers on the forum. In a story like this, you've got to pick on some innocent party.

c = f**2/(N*h)I hope we can all agree that all the terms on the right hand side of the equation are related to the lens and have nothing to do with camera format. --------------------------------------------------------------------------------------------

I believe most photographers would NOT agree that this equation has nothing to do with camera format, because most photographers consider the lens focal length and the camera format to be closely related.

If I decide to take a picture of a certain object from a certain location and I have a camera of a certain format, I will certainly try to choose the lens focal length to fill the frame. If I switch to a different format, this means choosing a lens of a different focal length. Yes, I could use a short lens on a large format and crop the image, but I will try to avoid doing this if possible. I would prefer to use a longer lens to fill the frame and then stop the lens down more to get the required DoF.

I know you disagree with this conceptual linking of format and lens, but this sort of disagreement is just semantics, with no real content, and it is getting tiresome. Can we agree that DoF is the same if I use the same lens and crop the larger format, but that DoF is not the same if I use a different lens to give the same field of view on a different format? If we agree on this, then it does not really matter if we disagree on vague statements like "format does not affect DoF".

c = f**2/(N*h)I hope we can all agree that all the terms on the right hand side of the equation are related to the lens and have nothing to do with camera format. --------------------------------------------------------------------------------------------

I believe most photographers would NOT agree that this equation has nothing to do with camera format, because most photographers consider the lens focal length and the camera format to be closely related.

If I decide to take a picture of a certain object from a certain location and I have a camera of a certain format, I will certainly try to choose the lens focal length to fill the frame. If I switch to a different format, this means choosing a lens of a different focal length. Yes, I could use a short lens on a large format and crop the image, but I will try to avoid doing this if possible. I would prefer to use a longer lens to fill the frame and then stop the lens down more to get the required DoF.

I know you disagree with this conceptual linking of format and lens, but this sort of disagreement is just semantics, with no real content, and it is getting tiresome. Can we agree that DoF is the same if I use the same lens and crop the larger format, but that DoF is not the same if I use a different lens to give the same field of view on a different format? If we agree on this, then it does not really matter if we disagree on vague statements like "format does not affect DoF".[a href=\"index.php?act=findpost&pid=81176\"][{POST_SNAPBACK}][/a]

Belive what you will. I certainly can't change that. Only you can do that.

I think the equations are for lenses, not just camera lenses. I do agree that most photographers tend to think in terms of the camera(s) and lens(es) they have. I just don't see the need for one set of rules for each camera and lens.

If lens focal length is linked to format, how is it I can put a 150mm lens on APS, 35mm, 645, 6x6, 4x5 camera? And they all produce the same focused image, just more or less of the world? I even once put my 6x6 50mm lens on my 4x5 camera. Same lens, different format camera and all the "laws of optics" went right along. There were other problems, but DoF was not one of them.

If your goal is to fill the frame, then, yes, I agree it is a good idea to know the frame size and have a bunch of focal lengths on hand. My goal is to produce an image for a print. This only requires the format to be 1) big enough to get the photo I want on it, and 2) I have a format that will do that. These are not always possibel for me. I can't photograph everything. But that is a hardware problrm, not a DoF problem. Sometime it can be equipmant if I need f/90 to get the DoF I want (planning). That is a lens problem and a plan problem, not a DoF problem. Not every plan is actually workable with the equipmant I have. I don't see any use in planning a print I can't take. Even if you can. But then scrambling around, zooming in and out, set the f/stop to max sharpness, let my camera focus (some how), set an exposure somehow, and then bracket like crazy isn't my idea of a solution or a plan either.

If your goal is to amke only 30cm prints from full frame negatives to be viewed by an average person under average conditions at 50cm, then maybe on-line calcualtors are just what the doctor ordered, for you. Please just don't say they are for everyone and every combination of conditions

Can we agree that DoF is the same if I use the same lens and crop the larger format, but that DoF is not the same if I use a different lens to give the same field of view on a different format? If we agree on this, then it does not really matter if we disagree on vague statements like "format does not affect DoF".[a href=\"index.php?act=findpost&pid=81176\"][{POST_SNAPBACK}][/a]

Well, I certainly can't agree with that. It's quite possible to get the same DoF when using a different lens on a different format shooting from the same distance, if you make an f stop adjustment.

An example would be the 20D with a 50mm lens at f5.6 and the 5D with 80mm lens at f9 (approximately). Because of the different pixel densities (and pixel count) of the 2 formats the precise difference in f stops would probably be in fractions not available in the camera settings. In this example, multiplying the 50mm focal length, and whatever f stop used, by 1.6 gives a good approximation.

I can't agree that DoF on a print is the same if I use the same lens (and presumably you mean same f stop and distance to subject) and crop the image, because the print will be different. As I've already tried to explain, the print from the uncropped image (negative) might contain lots of fuzzy elements giving the impression of a shallow DoF. The print from the cropped image might be tack sharp from corner to corner because all the fuzzy elements have been cropped out.

The only thing about DoF that format doesn't and cannot change is the mathematical description of it which is infinitely bigger than any physical format. It stretches all the way to infinity .

"... separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to re-write an equation so that each of two variables occurs on a different side of the equation."

Format on one side, DoF on the othr. Change format and only format and watch the change in DoF. Only problems here, some don't believe the math, and format doesn't appear opposite DoF - not related. Sure, you can replace c woth CoC (CoC=c8enlergement) and you still don't get format.

One might also look at if I change DoF (and only DoF), how does format change? Doesn't, not related.

c = f**2/(N*h)I hope we can all agree that all the terms on the right hand side of the equation are related to the lens and have nothing to do with camera format. --------------------------------------------------------------------------------------------

I believe most photographers would NOT agree that this equation has nothing to do with camera format, because most photographers consider the lens focal length and the camera format to be closely related.

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EricV, I think most people used to believe the earth was flat, the earth was the center of the universe, and Zeus was sitting on top of Olympus as king of the gods.

I don't think most people believe all that now, nor do I belive there was a major restructuring done to make those things untrue. They just weren't true to begin with, regardless of how many and who believed it. But I also belive the changes in beliefs were hard to make. Poor Gallileo.

Good comments, EricM. This discussion is getting ridiculous. Everyone agrees on all the equations, meaning we really do understand DoF and can use it properly in our photography. The only disagreements concern the language used to discuss it.

If I work by first selecting a lens, then adjusting the f/stop to give the DoF I desire for the final print I intend to make (using the equations we all agree on), then I am entitled to say "format does not affect DoF" (as long as it covers the field of view I am interested in and I don't mind cropping).

If I work by first selecting a film format, then choosing a lens to capture the field of view I am interested in, then adjusting the f/stop to give the DoF I desire for the final print I intend to make (using the equations we all agree on), then I am entitled to say "format affects DoF". Or maybe I have to say "format determines lens focal length which affects lens f/stop" to avoid offending anyone.

In both cases, if we all intend to make the same print, with the same field of view and the same depth of field, we will all end up choosing the same f/stop if we happen to use the same lens (independent of format), and we all agree we will have to use different f/stops to achieve similar DoF if we happen to select different lenses (driven by our choice of format).

Maybe, just maybe, we can all agree on this? In any case, I don't think there is really much more to discuss.

If I work by first selecting a film format, then choosing a lens to capture the field of view I am interested in, then adjusting the f/stop to give the DoF I desire for the final print I intend to make (using the equations we all agree on), then I am entitled to say "format affects DoF". Or maybe I have to say "format determines lens focal length which affects lens f/stop" to avoid offending anyone.

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Oh, I would agree with this. If I assume DoF is format dependant, it is far easier to prove I am right. And you are right within your assumptions

Where you may get in difficulty, is changing those assumption as you go, Like making less than a full frame enlargement. I frequently (maybe always) figure on using only about 90% of the available format to give myself some wiggle room later. This works but I have never been able to get that part of the image that falls just outside the film.

And working my way, I can also plan a full frame enlargement into a 30cm print to be viewed from 50cm by the average person

I find it easy to go from the general to the particular case, but not always possible to go the other way.

If I work by first selecting a lens, then adjusting the f/stop to give the DoF I desire for the final print I intend to make (using the equations we all agree on), then I am entitled to say "format does not affect DoF" (as long as it covers the field of view I am interested in and I don't mind cropping).

Maybe part of the confusion is due to the different work flow and procedures some people follow in making a picture. Personally speaking, I always look for the picture first. All pictures are bound within a format. I then select an approprite lens and distance to subject and make a crop. I always make a crop. It is impossible not to do so. A picture is by definiotion a crop. A cropless, formatless picture is an impossibility.

Sometimes it is impossible to take the picture because (1) the camera's format is too small, (2) I haven't got a lens wide enough, (3) I can't get far enough away from, or sufficiently close to, the subject.

The DoF mathematical formulas encompass the total range of possible (as well as impossible) pictures that can be made when shooting from a particular position. The number is infinite. You choose one and one only at a particular moment at a particular position when taking a picture. All characteristics of that one chosen picture are affected by format, including DoF. A picture cannot exist outside of a format. It's the choice of format that nails the selection of DoF since the scene in front of you, from the perspective of your lens (or position of your lens), will contain the whole range of DoF possibilities. Within that range, there are some pictures that are completley OOF, some that are completely sharp from corner to corner and some that are a mixture.

The making of a picture involves a subjective choice. The DoF formulas of course do not know the size of the image circle of your lens, or the sharpness of your lens, or the pixel density of your sensor, or anything about your choices. The DoF formulas are merely presenting the range of choices. If that's all Howards is saying, then of course I agree with him. I actually thought he was talking about making pictures and how the perception of DoF on the print (or negative for that matter) is affected by format.

Format on one side, DoF on the othr. Change format and only format and watch the change in DoF. [a href=\"index.php?act=findpost&pid=81188\"][{POST_SNAPBACK}][/a]

Unfortunately, it is usually impossible in practice to change to a smaller format without changing one of the- field of view- focal lengththat one got with one's usual procedure with a larger format.

For example, if I have photographed a certain scene with my 35mm film camera, choosing a focal length to more or less fill the frame with the desired subject matter, then using the same focal length with my 4/3 format DSLR will give a far narrower FOV, recording only about one quarter of the original subject area. Thus,

the smaller format forces me to use a shorter focal length in order to get the same composition as I previously got with the larger format.

There is the alternative of going back to the larger format and matching the FOV and DOF of the smaller format by using this same new shorter focal length and then cropping heavily, but that is not the situation that I or most photographers are interested in when we ask how DOF will be affected by changing to a smaller format.

P. S. If one wants formulas, one is2*tan(AFOV/2) = (format diagonal length)/(focal length)where AFOV is angular field of view of the image recorded by the sensor/film, measured on the diagonal.(There are similar ones got by replacing "diagonal" by "horizontal" or "vertical" thoughout.)

the smaller format forces me to use a shorter focal length in order to get the same composition as I previously got with the larger format.

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I don't disagree with that. But I can reduce the focal length without changing format to get the same image, just more of it. One more time (and last), if you assume format is a factor by insisting that the film not be cropped and the entire photo you had in mind (planned) fits on the film, then it is easy to prove a format dependance.

The smaller format you were speaking of seems to fail one condition for planning an image, namely the format selected out of necessity (what I have) be big enght to get the planned photo on. A 6x6 with a 159mm lens is plenty large enogh to get all the image on the film that an APS camera with a 150mm lens is. But if I make my plans with a 6x6 and then decide to use an APS, the 150mm lens might not work. I may have to switch my plan to a shorter focal length, or back up. BUT, I have changed my plan, and if I change the ground rules, I may have to change a lot of factors. That doesn't make DoF format dependant.

If I change formats, and then lens focal length (or focus distance) to get the photo back into the format, DoF calcs need to be redone, nnot because of the format change, but because I changed focal length (or distance).

The actual scene being photographed may not meet all the plans. When I go to the Grand Canyon, I don't plan a full width image of the Canyon. I don't have a lens that wide. I could plan that shot assuming a fisheye lens, but that would be a waste of time because I don't have one. Likewise, a plan may require f/1.4 to get the narrow DoF I would like. That is interesting, but since I don't have any f/1.4 lenses, not an implementable plan, as is.

If I had to change formats to get all of the Grand Canyon in, would the Grand Canyon become format dependant? If I don't have the equipment or it isn't even available, does that make the Grand Canyon unphotograhable? No, just certain planned images. I can make a plan that would reuire a 15mm lens at f/1.4 on an 8x10 camera. Doesn't mean I can do it. (And I chose an 8x10 camera not for DoF, but as big enough to get on film. That is still an inportant and necessary factor. But if I had that lens and an 11x14 camera, I could still get the same shot with the very same DoF as planned for the 8x10 camera.)

You need to be very careful when changing variables that you do not couple them with othr variables, and then attribute all or part of the change to the origianl variable. That is, if you change format and lens focal length and get a different DoF, don't attribute that change to format.

I can reduce the focal length without changing format to get the same image, just more of it.

That is not the same image: it is a different image, covering a larger FOV, that contains the prevoius smaller format image as only a part of the whole. A "head shot" is not the same image as a full length portrait.

Quote

One more time (and last), if you assume format is a factor by insisting that the film not be cropped and the entire photo you had in mind (planned) fits on the film, then it is easy to prove a format dependance.[a href=\"index.php?act=findpost&pid=81354\"][{POST_SNAPBACK}][/a]

And one more time, I am making no assumptions: I am stating explicitly that I am interested in what happens when I photograph a given scene using most or all of the area covered by the respective sensor/film formats. This is no more an "assumption" than are other comparison conditions, like focusing on the same subject from the same distance.

You are a simply stating the true but rather uninteresting fact that a camera with a larger sensor or film format can be used to more or less mimic the results of a smaller format, by suitable cropping.

Indeed one could use a 5D with 24x36mm format sensor and crop to the roughly 13.1x17.5mm format of the E-1, and have a rather heavy, expensive way to get 3.4MP images in the 13.1x17.5mm format of 4/3".

Yes, that cropped image has format 13.1x17.5mm, not 24x36mm, even if the camera is capable of producing images of larger formats when used with other cropping choices.

Or one could us the D2X with its 15.7x23.5mm sensor in high speed mode, which records an image from about a 12x18mm portio of the sensor: what format is that image? I would say it is 12x18mm, and I would say the same if one used normal mode, recorded a 15.7x23.5mm image and the cropped it to the same framing given by high speed mode.

How about we describe the format of an image as the height and width of the image formed in the focal plane of the camera and used to make the final print. Then when we crop, the cropped image is has a new, smaller format. Then it is clear that when photographing the same scene (FOV, subject distance, focus distance) using an image of smaller format, the aperture ratio must be reduced in proportion to the linear size of the image format in order to get the same DOF, while using the same f-stop with that smaller image format gives more DOF.

And one more time, I am making no assumptions: I am stating explicitly that I am interested in what happens when I photograph a given scene using most or all of the area covered by the respective sensor/film formats. This is no more an "assumption" than are other comparison conditions, like focusing on the same subject from the same distance.

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My mistake. I was interchanging a problem given (clearly stating the format selected is completely filled with only the photo I want) with an assumption. In fact, that mwakes it even easier. No need to assume DoF is format dependant, I am told it is. "It is because I said so." That makes even possible to prove pigs can fly. "Given pigs can fly at 100 mph, how long will it take a pig to fly 200 miles?"

Wrong of me to do that. However, I don't think it changes much of the discussion. Just the difference in what is an assumption and what is a given.

The I guess that lens makers are not "assuming" a value of CoC. It is just a "given" not stated very clearly.

No need to assume DoF is format dependant, I am told it is. "It is because I said so." That makes even possible to prove pigs can fly. "Given pigs can fly at 100 mph, how long will it take a pig to fly 200 miles?"[a href=\"index.php?act=findpost&pid=81364\"][{POST_SNAPBACK}][/a]

Howard, your analogy is ridiculously irrelevant. It turns on asserting a falsehood. (At least, I take it that you intend it to be clearly false that pigs can fly at 100 mph. If instead pigs can do that, there is no point to your analogy, and the answer is two hours, as surely as my answer is that DOF at equal aperture ratio increases.)

Where is the false assertion or assumption in my argument?

All I see in my argument is th statement that I am considering the quite real case of photographs taken with the larger format camera composed to fill most or all of the frame with the desired subject matter, so that little or no cropping is needed. This happens far more often than pigs fly at 100mph without mechanical assistance.